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Topic: What are "wavelets" ? (Read 6763 times) previous topic - next topic
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What are "wavelets" ?

I see a lot of people talking about Wavelets and support for wavelets.

Can somebody explain what wavelets are, how they work, and what their benefits are - preferably in normal english

What are "wavelets" ?

Reply #1 –
Wavelet is a type of compression which is usually applied at image compression such as Lurawave. If I'm not mistaken JPEG2000 use this kind of compression too instead of using macro block 8x8 in JPEG. Some video encoders also use this (dunno which).

In audio compression, there are only few of them that use this compression and usually for streaming.

May be someone more expert can explain about the algorithm and correct may mistake (if any)? Actually I don't know much about this.

What are "wavelets" ?

Reply #4 –
Really helpful for me since I've been lookin' for this with no result.
Thanx for the link.

What are "wavelets" ?

Reply #5 –
Quote
correct may mistake (if any)? Actually I don't know much about this.


I updated that post and included some links to exact places where you can learn about wavelets and understand the exact mechanism behind them. I also included a link for those who are interested in the Statistical Equation for a MDCT filterbank.You may alternativly search the NEC Research Index if you are looking for more documentation, etc. There is much research for wavelets there.


http://www.hydrogenaudio.org/forums/showth...=&threadid=2859
budding I.T professional

What are "wavelets" ?

Reply #6 –
Quote
Originally posted by mp3chan

In audio compression, there are only few of them that use this compression and usually for streaming.


Can you give an example of something that uses wavelets in audio coding?

What do wavelets have to do with streaming?

--
GCP

What are "wavelets" ?

Reply #7 –
Quote
Originally posted by Garf
Can you give an example of something that uses wavelets in audio coding?


AdaptedWave did
http://www.adaptedwave.com/

But seems to be gone now.

Some info survived:
http://web.archive.org/web/20010201145500/...daptedwave.com/ and
http://web.archive.org/web/20010517222437/...daptedwave.com/

Quote
What do wavelets have to do with streaming?


The target market of AdaptedWave was streaming, IIRC.

What are "wavelets" ?

Reply #8 –
Quote
Originally posted by Garf


Can you give an example of something that uses wavelets in audio coding?

What do wavelets have to do with streaming?

-- 
GCP


also this:
http://www.igd.fhg.de/igd-a9/research/audio/wam.html

Wavelets do compression with streaming.

What are "wavelets" ?

Reply #9 –
(sorry for bumping up an old thread here but I thought this is an interesting topic to post)

To my knowledge, wavelets in audio coding have found no particular advantage over subband coding, hence there is lesser research literature on audio coding when compared with image and video coding where indeed, wavelets have found a place.  The EZW (embedded zerotree wavelet) and SPIHT (set partitioning in hierarchical trees) algorithms used in image coding represent the state of the art. 

Wavelets are a special type of function which can be expanded (dilation) and shifted.  They serve the role of being a good basis function, much like the role that sines and cosines play in the DFT (discrete Fourier transform) and cosines in the DCT.  However, sines and cosines are rather constrained as they aren't flexible enough to track transient changes and frequency at the same time. ie.  Sharp transients need high frequency to detect but that sacrifices on long term trends and vice versa.  Hence the compromise between time and frequency resolution is fixed. 

Wavelets on the other hand allow multiple resolutions via different scaling (dilations and expansions).  Short wavelets pinpoint the sharp transients while long wavelets focus on the long trends in a signal.  Thus multiple resolutions of the signal are shown together.  So we can see the forest as well as the trees, so to speak.

It turns out that the discrete version of the wavelet decomposition resembles the filter bank algorithm of subband coding so that is why SBC and wavelets are often used synonymously.  The only difference is the background theorty between the two (one is a band splitter, the other is a multiresolution basis) and the filter coefficients.